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CHAPTER 1
MEASUREMENT AND PROBLEM SOLVING
Remind students that their answers to oddnumbered exercises may be slightly different from those given
here because of rounding.
Refer to ProblemSolving Hint: The "Correct" Answer in Chapter 1.
1.
(b).
2.
(c).
3.
(c).
4.
(a) Since 1 gal = 3.785 L,
300 L = (300 L)
×
= 79.3 gal.
.
(b) Since 1 in. = 2.54 cm,
225 cm = (225 cm)
×
= 88.6 in. = 7 ft 5 in.
.
.
(c) Since 1 m = 3.28 ft,
120 m
2
= (120 m
2
)
×
3.28 ft
1 m
2
= 1.29
×
10
3
ft
2
.
.
5.
(b)
6.
Since 1 in. = 2.54 cm,
3 cm = (3 cm)
×
= 1.2 in.
That would have been a huge lady bug.
.
Since 1 kg is equivalent to 2.2 lb.,
10 kg = (10 kg)
×
=22 lb.
Salmon are quite large.
7.
The decimal system (base 10) has a dime worth 10¢ and a dollar worth 10 dimes, or 100¢.
By analogy, a
duodecimal system would have a dime worth 12¢ and a dollar worth 12 “dimes,” or $1.44 in decimal
dollars.
Then a penny would be
of a dollar.
8.
(a) Different ounces are used for volume and weight measurements.
16 oz = 1 pt is a volume measure
and 16 oz = 1 lb. is a weight measure.
(b) Two different pound units are used.
Avoirdupois lb. = 16 oz‚ troy lb. = 12 oz.
9.
That is because 1 nautical mile = 6076 ft = 1.15 mi.
A nautical mile is larger than a (statute) mile.
10.
(d).
11.
(d).
12.
, it only tells if the equation is dimensionally correct.
13.
(c).
14.
Dividing something is equivalent to multiplying by the reciprocal.
m/s
÷
s =
×
=
.
Chapter 1
Measurement and Problem Solving
1
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View Full Document15.
Dimensional analysis uses the fundamental dimensions of physical quantities such as, length ([L]), mass
([M]), and time ([T]).
Unit analysis uses a specific system of units.
For example, if the mks system is
used, then meter (m), kilogram (kg), and second (s) are used in unit analysis.
16.
[L] = [L] +
×
[T] = [L] + [L].
17.
(d).
18.
[T] = = = [T].
The equation is dimensionally correct.
19.
m
2
= (m)
2
= m
2
.
20.
, since
[m
3
] = [m]
3
= [m
3
].
21.
.
V
= 4
π
r
3
/3 = 4
π
(8
r
3
)/24 = 4
π
(2
r
)
3
/24 =
π
d
3
/6.
So it should be
.
22.
x
=
g
= .
So the units of
g
are .
23.
, because
m/s
≠
m/s – (m/s
2
)(s)
2
= m/s – m.
24.
Since
ρ
= , the unit of mass is kg, and the unit of volume is m
3
, the unit of
is equal to
= .
25.
, because
[L
2
] =
[L]([L] + [L]) = [L
2
] + [L
2
].
26.
, because
m/s =
=
= m/s.
27.
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 Spring '08
 yuri
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